Discuss about the Matrix Systems?  Please answer at your own words.

The coplanar force system shown has a resultant of 400N acting in the direction toward a point with coordinates (5,6). Determine the characteristics of the unknown force W.

Please solve and show full work.

I need help with this problem. For 1a and 1b, I want to see how to do total differential. And for 1c, I want to see -1 in the relationship between the partial derivatives.

Sketch how water curls down a sink, say, in clock-wise rotation. Draw the resulting vector of the curl-operator applied on this water flow.

Please solve last two parts

Find the derivative of each function at the given point and interpret the physical meaning of this quantity. Include units in your answer  The gravitational force of attraction between two masses separated by a distance of x meters is inversely proportional to thesquare of the distance between them, which implies that the forceis described by the function F(x) = k/x2, for some constant k,where F(x) is measured in newtons. Find F′(10), expressing youranswer in terms of k

[c]

The system consists of the two smooth spheres, each weighing 5 lb and connected by a light spring, and the two bars of negligible weight hinged freely at their ends and hanging in the vertical plane. The spheres are confined to slide in the smooth horizontal guide. If a horizontal force F = 19 lb is applied to the one bar at the position shown, what is the acceleration of the center C of the spring? Does the result depend on the dimension b? Assume d = 18 in. www.xx C Answer: a = i d 9 F ft/sec²

You can use methods such as variation of parameters, application of exponential shift theorem, and evaluation of some inverse differential operators.